## Abstract

Using plausibility arguments, Mandelstam has shown that the solutions of the Bethe-Salpeter equation in the ladder approximation have branch points in the coupling constant g complex plane. This information is vital for the understanding of the analytic properties and the convergence properties of infinite sums of Feynman diagrams. In this paper we develop a formalism which permits an exact analysis of the coupling constant branch point location for approximate Bethe-Salpeter Pseudopotential equations with nonlocal Pseudopotentials. We apply this formalism to the two-nucleon interaction with the pseudoscalar pion exchange. Exact analytic expressions are found for the g 2^{2}/4π branch points which are confirmed by a computer test. The branch point position does not depend either on the pion and nucleon masses, or on the total energy.

Original language | English |
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Pages (from-to) | 487-500 |

Number of pages | 14 |

Journal | Nuclear Physics A |

Volume | 260 |

Issue number | 3 |

DOIs | |

State | Published - 12 Apr 1976 |